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Statistically Recognize Faces Based on Hidden Markov Models. Presented by Timothy Hsiao-Yi Chin Rahul Mody. What is Hidden Markov Model?. Its underlying is a Markov Chain.

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Statistically Recognize Faces Based on Hidden Markov Models

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## Statistically Recognize Faces Based on Hidden Markov Models

Presented by

Timothy Hsiao-Yi Chin

Rahul Mody

E6886 Project

## What is Hidden Markov Model?

Its underlying is a Markov Chain.

An HMM, at each unit of time, a single observation is generated from the current state according to the probability distribution, which is dependent on this state.

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### Mathematical Notation of HMM

• Suppose that there are T states {S1, …, ST} and the probability between state i and j is Pij. Observation of system can be defined as ot at time t. Let bSi(oi) be the probability function of ot at time t. Lastly, we have the initial probability , i = 1, …, n of Markov chain. Then the likelihood of the observing the sequence o is

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### Which probability function of ot?

• In HMM framework, observation o is assumed to be governed by the density of a Gaussian mixture distribution.

• Where k is the dimension of ot, and where oiand

are the mean vector and covariance matrix, respectively

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70%

60%

25%

28%

5%

12%

70%

10%

20%

Sunny

Rainy

Snowy

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### Represent it as a Markov Model*

• States:

• State transition probabilities:

• Initial state distribution:

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### What is sequence o in this example?*

• Sequence o:

• The probability could be computed by the conditional probability:

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5%

70%

80%

20%

20%

Sunny

60%

Rainy

15%

38%

2%

5%

5%

75%

10%

75%

Snowy

20%

45%

5%

50%

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### What other parameters will be needed?

• If we can not see what is inside blue circle, what can we actually see?

• Observations:

• Observation probabilities:

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### Forward-Backward Algorithm: Forward

• If Observation probability is

• then

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### Forward-Backward Algorithm: Backward

• If there is a

• Then

• The Forward-Backward Algorithm tells us that

• for any time t

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### Face identification using HMM

• An Observation sequence is extracted from the unknown face, the likelihood of each HMM generating this face could be computed.

• In theory, the likelihood is

• The maximum P(O) can identifies the unknown faces.

• However, it takes too much time to compute.

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### Face identification using HMM

• In practice, we only need one S sequence

which maximizes

• This is a dynamic programming optimization procedure.

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### Viterbi Algorithm

• Given a S sequence, a dynamic programming approach to solve this problem

• where

• By induction, the max Probability in state i+1 at time t+1 is based on the max probability in state I at time t.

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### Algorithm itself

• Initialization

where denotes the collection of that sequence which is based on max

• Recursion:

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### Algorithm itself (2)

• Termination

• Sequence constructing from T to t

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### Face Detection

• In simple face recognition framework, the picture is assumed to be a frontal view of a single person and the background is monochrome.

• This project assumes that with the techniques of face detection, the performance of face recognition may be better than the approach presented above.

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### Acknowledgement

• The authors of this presentation slides would like to give thanks to Dr. Doan, UIUC.

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### Reference

• [1] Ferdinando Samaria, and Steve Young, HMM-based architecture for face identification.

• [2] Jia, Li, Amir Najmi, and Robert M. Gray, Image Classification by a Two-Dimensional Hidden Markov Model

• [3] Ming-Hsuan Yang, David J. Kriegman, Narendra Ahuja, Detecting Faces In Images: A survey

• [4] T.K. Leung, M. C. Burl, and P. Perona, Finding Faces in Cluttered Scenes using Random Labeled Graph Matching

• [5] James Wayman, Anil Jain, Davide Maltoni, and Dario Maio, Biometric Systems, Springer, 2005

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